Solve the system of equations. y = 10x - 80 y = x^2 - 12x + 41 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______)

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Solve the system of equations. y = 10x - 80 y = x^2 - 12x + 41    Write the coordinates in exact form. Simplify all fractions and radicals. (______,______)

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Substitute y Equation: Substitute y from the first equation into the second equation. Since y = 10x - 80, we can replace y in the second equation y = x^2 - 12x + 41 with 10x - 80. This gives us the equation 10x - 80 = x^2 - 12x + 41.Rearrange and Solve for x: Rearrange the equation to set it to zero and solve for x. This means we will subtract 10x and add 80 to both sides of the equation. The new equation is 0 = x^2 - 12x + 10x + 41 - 80, which simplifies to 0 = x^2 - 2x - 39.Factor Quadratic Equation: Factor the quadratic equation x^2 - 2x - 39. We are looking for two numbers that multiply to -39 and add up to -2. The numbers that satisfy these conditions are -9 and +7, so we can factor the equation as (x - 9)(x + 7) = 0.Solve for x: Solve for x by setting each factor equal to zero. This gives us two possible solutions for x: x - 9 = 0 or x + 7 = 0. Solving these, we get x = 9 or x = -7.Substitute x for y: Substitute x back into the original equation y = 10x - 80 to find the corresponding y values. First, for x = 9, we get y = 10(9) - 80, which simplifies to y = 90 - 80, so y = 10.Find y Values: Now, for x = -7, we substitute into y = 10x - 80 to get y = 10(-7) - 80, which simplifies to y = -70 - 80, so y = -150.Final Solutions: We now have two solutions for the system of equations: (9, 10) and (-7, -150). These are the coordinates of the points where the two equations intersect.

Solve the system of equations. $\newline$ $y = 10x - 80$ $\newline$ $y = x^2 - 12x + 41$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,)

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Solve the system of equations.\newliney=10x−80y = 10x - 80y=10x−80\newliney=x2−12x+41y = x^2 - 12x + 41y=x2−12x+41\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

Solve the system of equations. $\newline$ $y = 10x - 80$ $\newline$ $y = x^2 - 12x + 41$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,)